Question

How much work must be done in the car to slow it from 100km/h to 50km/h

Answer 1

Work done=376.22MJ

Step-by-step explanation:

The following problem can be solved using work-energy theorem

Work-Energy Theorem:

For system of particles

∑Wext+ ∑Wint= ΔK

where ∑Wext is the work done by the external forces on the system and ∑Wint is the work done by internal forces on the system. Newton's third law of motion gives you that ∑Fint=0, but the work done by internal forces may or may not be 0.

• positive work increases the kinetic energy and negative work decreases the kinetic energy.
• Work can be converted into kinetic energy and kinetic energy can be converted into work.

now coming back to our problem

`v`1=
`50km/h=13.89m/s`

`v`2=
`100km/h=27.78m/s`

Let us assume that average mass of the car(m) is
`1300kg` and ∑Wint=0J

Therefore, Work done(W)=ΔK

=K₂-K₁

=
`(1)/(2)m(v1)^(2)-(1)/(2)m(v2)^(2)`

=
`(1)/(2)*1300*(13.89)^(2)-(1)/(2)*1300*(27.78)^(2)`

=376.22KJ